@AviK
Engel v. Vitale
said that the schools/government could not compose or have an official prayer to be said in public school. It did not ban organized prayer. I did not forget about it, It was not on point.
Furthermore, it doesn’t matter who file amicus briefs, only the court could have banned the organized prayer in response to the suits, not organized Jewish secular groups.
Rockstar gets an F.
It would be far more likely that organized secular groups could influence legislatures to change laws, than the court to rule something unconstitutional.